Challenge Level

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Challenge Level

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Challenge Level

Can you cut up a square in the way shown and make the pieces into a triangle?

Challenge Level

Can you split each of the shapes below in half so that the two parts are exactly the same?

Challenge Level

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Challenge Level

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Challenge Level

Make a flower design using the same shape made out of different sizes of paper.

Challenge Level

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

Challenge Level

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Challenge Level

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Challenge Level

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Challenge Level

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Challenge Level

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Challenge Level

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Challenge Level

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Challenge Level

Can you make five differently sized squares from the interactive tangram pieces?

Challenge Level

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

Challenge Level

Exploring and predicting folding, cutting and punching holes and making spirals.

Challenge Level

What is the greatest number of squares you can make by overlapping three squares?

Challenge Level

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Challenge Level

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Challenge Level

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

Challenge Level

Reasoning about the number of matches needed to build squares that share their sides.

Challenge Level

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

Challenge Level

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Challenge Level

Can you visualise what shape this piece of paper will make when it is folded?

Challenge Level

Make a cube out of straws and have a go at this practical challenge.

Challenge Level

Can you make the birds from the egg tangram?

Challenge Level

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Challenge Level

What shape is made when you fold using this crease pattern? Can you make a ring design?

Challenge Level

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Challenge Level

Follow these instructions to make a three-piece and/or seven-piece tangram.

Challenge Level

Follow these instructions to make a five-pointed snowflake from a square of paper.

Challenge Level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Challenge Level

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

Challenge Level

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Challenge Level

Did you know mazes tell stories? Find out more about mazes and make one of your own.

Challenge Level

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

Challenge Level

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

Challenge Level

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Challenge Level

These pictures show squares split into halves. Can you find other ways?

Challenge Level

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Challenge Level

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

Challenge Level

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Challenge Level

Can you put these shapes in order of size? Start with the smallest.

Challenge Level

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

Challenge Level

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Challenge Level

Can you each work out what shape you have part of on your card? What will the rest of it look like?

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.